You don't need an emergency fund until you have an emergency. If I were you, I would not dump my savings into the mortgage payment. By having an emergency fund, you probably are probably in a position to absorb a financial emergency.

To set my mind at ease, I would calculate how much longer it would take to pay off the mortgage at the rate you are paying it. Then I would recalculate how much I would have to increase the payments to pay off 12 months earlier. Then I would make a decision of how much to pay off. If your mortgage doesn't have balloon payments, I would just maintain your regular practice.